Finite Group Databasebeta

← #14322607

Subgroups — #14322607

Order 1920.

1344 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×#217C211yesmaximal, characteristic
2#11751045C211yesmaximal, characteristic, complemented
3C5×#4944C211yesmaximal, characteristic, complemented
4C3×#65244C211yesmaximal, characteristic
5#11749488C211yesmaximal, characteristic
6#11749481C211yesmaximal, characteristic, complemented
7#11749478C211yesmaximal, characteristic, complemented
8#11748885C211yesmaximal, characteristic, complemented
9#11748884C211yesmaximal, characteristic, complemented
10#11748878C211yesmaximal, characteristic, complemented
11Dic3×#685C211yesmaximal, characteristic, complemented
12#11748712C211yesmaximal, characteristic, complemented
13#11748709C211yesmaximal, characteristic, complemented
14#11748708C211yesmaximal, characteristic, complemented
15#11748706C211yesmaximal, characteristic, complemented
16#10607556—31nomaximal, Hall
17C24×C3×D5C2211yescharacteristic
18C22×D5×Dic3C2211yescharacteristic
19C22×D5×Dic3C2211yescharacteristic
20C2×C3×C5×C22⋊C4C2211yescharacteristic
21C2×#6719C2211yescharacteristic
22C2×#6719C2211yescharacteristic
23C2×#6712C2211yescharacteristic, complemented
24C2×C4×Dic15C2211yescharacteristic, complemented
25C2×C5×#217C2211yescharacteristic
26C2×C5×#217C2211yescharacteristic
27C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
28C2×C4×C5×Dic3C2211yescharacteristic, complemented
29C2×C3×C22⋊Dic5C2211yescharacteristic
30C2×C3×#685C2211yescharacteristic
31C2×C3×#685C2211yescharacteristic
32C2×C3×#685C2211yescharacteristic
33C2×C3×#685C2211yescharacteristic
34D5×#217C418yescomplemented
35C2×Dic3⋊Dic5C2211yescharacteristic, complemented
36C2×#6669C2211yescharacteristic, complemented
37C2×#6665C2211yescharacteristic
38C2×#6665C2211yescharacteristic
39C2×#6665C2211yescharacteristic
40C2×#6665C2211yescharacteristic
41C2×#6665C2211yescharacteristic
42C2×#6665C2211yescharacteristic
43C2×Dic3×Dic5C2211yescharacteristic, complemented
44C2×Dic3×Dic5C2211yescharacteristic, complemented
45#91115C2211yescharacteristic, complemented
46#91115C2211yescharacteristic, complemented
47C5×C3⋊#95C2211yescharacteristic, complemented
48C5×C3⋊#95C2211yescharacteristic, complemented
49#90994C2211yescharacteristic, complemented
50#90994C2211yescharacteristic, complemented
51#90994C2211yescharacteristic, complemented
52#90994C2211yescharacteristic, complemented
53#73820—51nomaximal, Hall
54C2×D5×C22⋊C4—31no—
55C5×#388—31no—
56#65279—31no—
57#65276—31no—
58#65244—31no—
59#65244D311yescharacteristic
60#65240—31no—
61#65234—31no—
62#65233—31no—
63#65229—31no—
64C4×#685—31no—
65#64959—31no—
66#64958—31no—
67#64956—31no—
68#64955—31no—
69C24×C3×C5C2311yescharacteristic
70C23×C3×D5—22no—
71C23×C3×D5—22no—
72C23×C3×D5—41no—
73C23×C3×D5—41no—
74C23×C3×D5—41no—
75C23×C3×D5—41no—
76C23×C3×D5C2×C414yes—
77C23×C3×D5C2311yescharacteristic
78C23×C3×D5C2311yescharacteristic
79C22×C3×C4×C5C2311yescharacteristic
80C22×C3×C4×C5C2311yescharacteristic
81C22×Dic15C2311yescharacteristic
82C22×Dic15C2311yescharacteristic
83C22×Dic15C2311yescharacteristic
84C22×Dic15C2311yescharacteristic
85C22×C5×Dic3C2311yescharacteristic
86C22×C5×Dic3C2311yescharacteristic
87C22×C5×Dic3C2311yescharacteristic
88C22×C5×Dic3C2311yescharacteristic
89C22×C3×Dic5C2311yescharacteristic
90C22×C3×Dic5C2311yescharacteristic
91C2×D5×Dic3—41no—
92C2×D5×Dic3—41no—
93C2×D5×Dic3—41no—
94C2×D5×Dic3—41no—
95C2×D5×Dic3C2×C414yes—
96C2×D5×Dic3C2×C414yes—
97C3×C5×C22⋊C4—41no—
98#6719—41no—
99#6719C2×C414yes—
100#6712—41no—
101C4×Dic15—41no—
102C5×#217—41no—
103C5×#217C2×C414yes—
104C5×Dic3⋊C4—41no—
105C4×C5×Dic3—41no—
106C3×C22⋊Dic5—41no—
107C3×#685—22no—
108C3×#685—22no—
109C3×#685—41no—
110C3×#685—41no—
111Dic3⋊Dic5—41no—
112#6669—41no—
113#6665—22no—
114#6665—22no—
115#6665—41no—
116#6665—41no—
117#6665C2×C414yes—
118#6665C2×C414yes—
119Dic3×Dic5—41no—
120Dic3×Dic5—41no—
121C22×#217—51no—
122C3×#379—51no—
123#5247—51no—
124#4945—51no—
125#4945—51no—
126#4945—51no—
127#4945—51no—
128#4944—51no—
129#4944—51no—
130#4944—51no—
131#4944D511yescharacteristic, complemented
132#4942—51no—
133#4942—51no—
134Dic3×C22⋊C4—51no—
135Dic3×C22⋊C4—51no—
136C24×D5C2×D311yescharacteristic
137C22×C4×D5—31no—
138C22×C4×D5—31no—
139C2×C5×C4⋊C4—31no—
140C2×C5×C22⋊C4—31no—
141C2×C5×C22⋊C4—31no—
142C2×C5×C22⋊C4C2×D311yescharacteristic
143C2×C42×C5—31no—
144C2×C22⋊Dic5—31no—
145C2×C22⋊Dic5—31no—
146C2×C22⋊Dic5C2×D311yescharacteristic
147C2×#685—31no—
148C2×#685—31no—
149C2×#685—31no—
150C2×#685—31no—
151C2×#685—31no—
152C2×#685—31no—
153C2×#685C2×D311yescharacteristic
154C2×#685C2×D311yescharacteristic
155C2×#685C2×D311yescharacteristic
156C2×#685C2×D311yescharacteristic
157C2×C4⋊Dic5—31no—
158C2×#683—31no—
159C2×#683—31no—
160C2×C4×Dic5—31no—
161C2×C4×Dic5—31no—
162C2×C4×Dic5—31no—
163D5×C22⋊C4—38no—
164C5×#95—31no—
165C5×#95—31no—
166#3963—31no—
167#3963—31no—
168#3963—31no—
169#3963—31no—
170#3963—31no—
171#3963—31no—
172#2312—151noSylow
173C23×C3×C5—21no—
174C23×C3×C5—21no—
175C23×C3×C5—21no—
176C23×C3×C5—21no—
177C23×C3×C5—21no—
178C23×C3×C5—21no—
179C23×C3×C5C22×C412yes—
180C23×C3×C5C2411yescharacteristic
181C22×C3×D5—21no—
182C22×C3×D5—21no—
183C22×C3×D5—21no—
184C22×C3×D5—21no—
185C22×C3×D5—21no—
186C22×C3×D5—21no—
187C22×C3×D5—21no—
188C22×C3×D5—21no—
189C22×C3×D5—21no—
190C22×C3×D5—21no—
191C22×C3×D5—28no—
192C22×C3×D5—44no—
193C22×C3×D5—44no—
194C22×C3×D5—44no—
195C22×C3×D5—44no—
196C22×C3×D5—44no—
197C22×C3×D5—44no—
198C22×C3×D5C22×C412yes—
199C22×C3×D5C22×C412yes—
200C22×C3×D5#4112yes—
201C22×C3×D5#4112yes—
202C2×C3×C4×C5—21no—
203C2×C3×C4×C5—21no—
204C2×C3×C4×C5—21no—
205C2×C3×C4×C5—21no—
206C2×C3×C4×C5—21no—
207C2×C3×C4×C5—21no—
208C2×Dic15—21no—
209C2×Dic15—21no—
210C2×Dic15—21no—
211C2×Dic15—21no—
212C2×Dic15—21no—
213C2×Dic15—21no—
214C2×Dic15—21no—
215C2×Dic15—21no—
216C2×Dic15—21no—
217C2×Dic15—21no—
218C2×Dic15C22×C412yes—
219C2×Dic15C22×C412yes—
220C2×C5×Dic3—21no—
221C2×C5×Dic3—21no—
222C2×C5×Dic3—21no—
223C2×C5×Dic3—21no—
224C2×C5×Dic3—21no—
225C2×C5×Dic3—21no—
226C2×C5×Dic3—21no—
227C2×C5×Dic3—21no—
228C2×C5×Dic3—21no—
229C2×C5×Dic3—21no—
230C2×C5×Dic3C22×C412yes—
231C2×C5×Dic3C22×C412yes—
232C2×C3×Dic5—21no—
233C2×C3×Dic5—21no—
234C2×C3×Dic5—21no—
235C2×C3×Dic5—21no—
236C2×C3×Dic5—21no—
237C2×C3×Dic5—21no—
238D5×Dic3—44no—
239D5×Dic3—44no—
240C25×C3—51no—
241C23×Dic3—51no—
242C23×Dic3—51no—
243C2×C3×C22⋊C4—51no—
244C2×C3×C22⋊C4—51no—
245C2×C3×C22⋊C4—51no—
246C2×C3×C22⋊C4—51no—
247C2×C3×C22⋊C4—51no—
248C2×C3×C22⋊C4C2×D511yescharacteristic
249C2×#217—51no—
250C2×#217—51no—
251C2×#217—51no—
252C2×#217—58no—
253C2×#217—51no—
254C2×#217—51no—
255C2×#217—51no—
256C2×#217—51no—
257C2×#217—51no—
258C2×#217C2×D511yescharacteristic
259C2×#217C2×D511yescharacteristic
260C2×Dic3⋊C4—51no—
261C2×Dic3⋊C4—51no—
262C2×Dic3⋊C4—51no—
263C2×Dic3⋊C4C2×D511yescharacteristic, complemented
264C2×C4×Dic3—51no—
265C2×C4×Dic3—51no—
266C2×C4×Dic3—51no—
267C2×C4×Dic3C2×D511yescharacteristic, complemented
268C3⋊#95—51no—
269C3⋊#95—51no—
270C3⋊#95—51no—
271C3⋊#95—51no—
272C3⋊#95—51no—
273C3⋊#95—51no—
274C3⋊#95C2×D511yescharacteristic, complemented
275C3⋊#95C2×D511yescharacteristic, complemented
276C24×C5C22×D311yescharacteristic
277C23×D5—22no—
278C23×D5—22no—
279C23×D5—41no—
280C23×D5—41no—
281C23×D5—41no—
282C23×D5—41no—
283C23×D5C4×D314yes—
284C23×D5C22×D311yescharacteristic
285C23×D5C22×D311yescharacteristic
286C22×C4×C5—31no—
287C22×C4×C5—31no—
288C22×C4×C5—31no—
289C22×C4×C5—31no—
290C22×C4×C5C22×D311yescharacteristic
291C22×C4×C5C22×D311yescharacteristic
292C22×Dic5—31no—
293C22×Dic5—31no—
294C22×Dic5—31no—
295C22×Dic5—31no—
296C22×Dic5C22×D311yescharacteristic
297C22×Dic5C22×D311yescharacteristic
298C2×C4×D5—34no—
299C2×C4×D5—34no—
300C2×C4×D5—121no—
301C2×C4×D5—121no—
302C2×C4×D5—121no—
303C2×C4×D5—121no—
304C5×C4⋊C4—121no—
305C5×C22⋊C4—34no—
306C5×C22⋊C4—41no—
307C5×C22⋊C4—121no—
308C42×C5—121no—
309C22⋊Dic5—34no—
310C22⋊Dic5—41no—
311C22⋊Dic5—121no—
312#685—22no—
313#685—22no—
314#685—34no—
315#685—34no—
316#685—41no—
317#685—41no—
318#685—62no—
319#685—62no—
320#685—121no—
321#685—121no—
322C4⋊Dic5—121no—
323#683—121no—
324#683—121no—
325C4×Dic5—121no—
326C4×Dic5—121no—
327C4×Dic5—121no—
328C22×C22⋊C4—151no—
329#388—31no—
330#388—151no—
331#388—151no—
332#388—151no—
333#388—151no—
334#388—151no—
335#388—151no—
336#388—151no—
337#380—151no—
338#380—151no—
339#379—51no—
340#379—151no—
341C4×C22⋊C4—151no—
342C4×C22⋊C4—151no—
343C22×C3×C5—22no—
344C22×C3×C5—22no—
345C22×C3×C5—22no—
346C22×C3×C5—41no—
347C22×C3×C5—41no—
348C22×C3×C5—41no—
349C22×C3×C5—41no—
350C22×C3×C5C23×C411yescharacteristic
351C22×C3×C5C2×#4111yescharacteristic
352C22×C3×C5C2×#4111yescharacteristic
353C22×C3×C5H(5,𝔽2)11yescharacteristic
354C22×C3×C5H(5,𝔽2)11yescharacteristic
355C22×C3×C5H(5,𝔽2)11yescharacteristic
356C22×C3×C5H(5,𝔽2)11yescharacteristic
357C2×C3×D5—22no—
358C2×C3×D5—22no—
359C2×C3×D5—22no—
360C2×C3×D5—22no—
361C2×C3×D5—22no—
362C2×C3×D5—22no—
363C2×C3×D5—22no—
364C2×C3×D5—22no—
365C2×C3×D5—22no—
366C2×C3×D5—416no—
367C2×C3×D5—41no—
368C2×C3×D5—41no—
369C2×C3×D5—41no—
370C2×C3×D5—41no—
371C2×C3×D5#11714yes—
372C3×C4×C5—41no—
373C3×C4×C5—41no—
374Dic15—22no—
375Dic15—22no—
376Dic15—41no—
377Dic15—41no—
378C3×Dic5—41no—
379C3×Dic5—41no—
380C5×Dic3—22no—
381C5×Dic3—22no—
382C5×Dic3—41no—
383C5×Dic3—41no—
384C24×C3—51no—
385C24×C3—51no—
386C24×C3—54no—
387C24×C3—102no—
388C24×C3—102no—
389C24×C3—201no—
390C24×C3—201no—
391C24×C3—201no—
392C24×C3—201no—
393C24×C3C22×D511yescharacteristic
394C22×C3×C4—51no—
395C22×C3×C4—51no—
396C22×C3×C4C22×D511yescharacteristic
397C22×C3×C4C22×D511yescharacteristic
398C22×Dic3—51no—
399C22×Dic3—51no—
400C22×Dic3—54no—
401C22×Dic3—54no—
402C22×Dic3—51no—
403C22×Dic3—51no—
404C22×Dic3—201no—
405C22×Dic3—201no—
406C22×Dic3—201no—
407C22×Dic3—201no—
408C22×Dic3C22×D511yescharacteristic
409C22×Dic3C22×D511yescharacteristic
410C22×Dic3C22×D511yescharacteristic
411C22×Dic3C22×D511yescharacteristic
412C3×C22⋊C4—41no—
413C3×C22⋊C4—102no—
414C3×C22⋊C4—102no—
415C3×C22⋊C4—201no—
416C3×C22⋊C4—201no—
417C3×C22⋊C4—201no—
418#217—41no—
419#217—54no—
420#217—54no—
421#217—54no—
422#217—102no—
423#217—102no—
424#217—201no—
425#217—201no—
426#217—201no—
427#217C4×D514yes—
428Dic3⋊C4—41no—
429Dic3⋊C4—201no—
430Dic3⋊C4—201no—
431Dic3⋊C4—201no—
432C4×Dic3—41no—
433C4×Dic3—201no—
434C4×Dic3—201no—
435C4×Dic3—201no—
436C23×C5—21no—
437C23×C5—21no—
438C23×C5—21no—
439C23×C5—21no—
440C23×C5—21no—
441C23×C5—21no—
442C23×C5C2×C4×D312yes—
443C23×C5C23×D311yescharacteristic
444C22×D5—21no—
445C22×D5—21no—
446C22×D5—21no—
447C22×D5—21no—
448C22×D5—21no—
449C22×D5—21no—
450C22×D5—21no—
451C22×D5—21no—
452C22×D5—21no—
453C22×D5—21no—
454C22×D5—28no—
455C22×D5—44no—
456C22×D5—44no—
457C22×D5—44no—
458C22×D5—44no—
459C22×D5—44no—
460C22×D5—44no—
461C22×D5C2×C4×D312yes—
462C22×D5C2×C4×D312yes—
463C22×D5#23712yes—
464C22×D5#23712yes—
465C2×C4×C5—21no—
466C2×C4×C5—21no—
467C2×C4×C5—21no—
468C2×C4×C5—21no—
469C2×C4×C5—21no—
470C2×C4×C5—21no—
471C2×C4×C5—32no—
472C2×C4×C5—32no—
473C2×C4×C5—61no—
474C2×C4×C5—61no—
475C2×C4×C5—61no—
476C2×C4×C5—61no—
477C2×C4×C5—61no—
478C2×C4×C5—61no—
479C2×C4×C5—61no—
480C2×C4×C5—61no—
481C2×C4×C5—61no—
482C2×C4×C5—61no—
483C2×Dic5—21no—
484C2×Dic5—21no—
485C2×Dic5—21no—
486C2×Dic5—21no—
487C2×Dic5—21no—
488C2×Dic5—21no—
489C2×Dic5—32no—
490C2×Dic5—32no—
491C2×Dic5—61no—
492C2×Dic5—61no—
493C2×Dic5—61no—
494C2×Dic5—61no—
495C2×Dic5—61no—
496C2×Dic5—61no—
497C2×Dic5—61no—
498C2×Dic5—61no—
499C2×Dic5—61no—
500C2×Dic5—61no—
501C4×D5—124no—
502C4×D5—124no—
503C25—51no—
504C23×C4—151no—
505C23×C4—151no—
506C2×C4⋊C4—31no—
507C2×C4⋊C4—151no—
508C2×C4⋊C4—151no—
509C2×C4⋊C4—151no—
510C2×C22⋊C4—31no—
511C2×C22⋊C4—31no—
512C2×C22⋊C4—51no—
513C2×C22⋊C4—51no—
514C2×C22⋊C4—51no—
515C2×C22⋊C4—51no—
516C2×C22⋊C4—51no—
517C2×C22⋊C4—158no—
518C2×C22⋊C4—151no—
519C2×C22⋊C4—151no—
520C2×C22⋊C4—151no—
521C2×C22⋊C4—151no—
522C2×C22⋊C4—151no—
523C2×C22⋊C4—151no—
524C2×C22⋊C4—151no—
525C2×C22⋊C4—151no—
526C2×C22⋊C4D3×D511yescharacteristic
527C2×C42—31no—
528C2×C42—151no—
529C2×C42—151no—
530C2×C42—151no—
531#95—31no—
532#95—31no—
533#95—151no—
534#95—151no—
535#95—151no—
536#95—151no—
537#95—151no—
538#95—151no—
539C2×C3×C5—42no—
540C2×C3×C5C2×#11711yescharacteristic
541C2×C3×C5#51811yescharacteristic
542C2×C3×C5#51811yescharacteristic
543C2×C3×C5#53811yescharacteristic
544C2×C3×C5#53811yescharacteristic
545C2×C3×C5#53811yescharacteristic
546C2×C3×C5#53811yescharacteristic
547C3×D5—24no—
548C3×D5—42no—
549C23×C3—21no—
550C23×C3—21no—
551C23×C3—21no—
552C23×C3—21no—
553C23×C3—21no—
554C23×C3—21no—
555C23×C3—52no—
556C23×C3—52no—
557C23×C3—52no—
558C23×C3—52no—
559C23×C3—108no—
560C23×C3—101no—
561C23×C3—101no—
562C23×C3—101no—
563C23×C3—101no—
564C23×C3—101no—
565C23×C3—101no—
566C23×C3—101no—
567C23×C3—101no—
568C23×C3—101no—
569C23×C3—101no—
570C23×C3—204no—
571C23×C3—204no—
572C23×C3—204no—
573C23×C3—204no—
574C23×C3—204no—
575C23×C3—204no—
576C23×C3C2×C4×D512yes—
577C23×C3C23×D511yescharacteristic
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—101no—
585C2×C3×C4—101no—
586C2×C3×C4—101no—
587C2×C3×C4—101no—
588C2×C3×C4—101no—
589C2×C3×C4—101no—
590C2×Dic3—21no—
591C2×Dic3—21no—
592C2×Dic3—21no—
593C2×Dic3—21no—
594C2×Dic3—21no—
595C2×Dic3—21no—
596C2×Dic3—21no—
597C2×Dic3—21no—
598C2×Dic3—21no—
599C2×Dic3—21no—
600C2×Dic3—52no—
601C2×Dic3—52no—
602C2×Dic3—101no—
603C2×Dic3—101no—
604C2×Dic3—101no—
605C2×Dic3—101no—
606C2×Dic3—101no—
607C2×Dic3—101no—
608C2×Dic3—101no—
609C2×Dic3—101no—
610C2×Dic3—101no—
611C2×Dic3—101no—
612C2×Dic3—204no—
613C2×Dic3—204no—
614C2×Dic3C2×C4×D512yes—
615C2×Dic3C2×C4×D512yes—
616C22×C5—22no—
617C22×C5—22no—
618C22×C5—22no—
619C22×C5—41no—
620C22×C5—41no—
621C22×C5—41no—
622C22×C5—41no—
623C22×C5C22×C4×D311yescharacteristic
624C22×C5C2×#23711yescharacteristic
625C22×C5C2×#23711yescharacteristic
626C22×C5#100411yescharacteristic
627C22×C5#100411yescharacteristic
628C22×C5#100411yescharacteristic
629C22×C5#100411yescharacteristic
630C2×D5—22no—
631C2×D5—22no—
632C2×D5—22no—
633C2×D5—22no—
634C2×D5—22no—
635C2×D5—22no—
636C2×D5—22no—
637C2×D5—22no—
638C2×D5—22no—
639C2×D5—416no—
640C2×D5—41no—
641C2×D5—41no—
642C2×D5—41no—
643C2×D5—41no—
644C2×D5#87714yes—
645C4×C5—41no—
646C4×C5—41no—
647C4×C5—62no—
648C4×C5—62no—
649C4×C5—121no—
650C4×C5—121no—
651Dic5—41no—
652Dic5—41no—
653Dic5—62no—
654Dic5—62no—
655Dic5—121no—
656Dic5—121no—
657C24—51no—
658C24—51no—
659C24—54no—
660C24—102no—
661C24—102no—
662C24—201no—
663C24—201no—
664C24—201no—
665C24—201no—
666C24C2×D3×D511yescharacteristic
667C22×C4—31no—
668C22×C4—31no—
669C22×C4—31no—
670C22×C4—31no—
671C22×C4—51no—
672C22×C4—51no—
673C22×C4—154no—
674C22×C4—154no—
675C22×C4—151no—
676C22×C4—151no—
677C22×C4—151no—
678C22×C4—151no—
679C22×C4—601no—
680C22×C4—601no—
681C22×C4—601no—
682C22×C4—601no—
683C22×C4C2×D3×D511yescharacteristic
684C22×C4C2×D3×D511yescharacteristic
685C4⋊C4—121no—
686C4⋊C4—601no—
687C4⋊C4—601no—
688C4⋊C4—601no—
689C22⋊C4—34no—
690C22⋊C4—41no—
691C22⋊C4—102no—
692C22⋊C4—102no—
693C22⋊C4—121no—
694C22⋊C4—154no—
695C22⋊C4—154no—
696C22⋊C4—154no—
697C22⋊C4—201no—
698C22⋊C4—201no—
699C22⋊C4—201no—
700C22⋊C4—302no—
701C22⋊C4—302no—
702C22⋊C4—601no—
703C22⋊C4—601no—
704C22⋊C4—601no—
705C42—121no—
706C42—601no—
707C42—601no—
708C42—601no—
709C3×C5#231211yescharacteristic, complemented, Hall
710C22×C3—22no—
711C22×C3—22no—
712C22×C3—22no—
713C22×C3—41no—
714C22×C3—41no—
715C22×C3—41no—
716C22×C3—41no—
717C22×C3—54no—
718C22×C3—102no—
719C22×C3—102no—
720C22×C3—102no—
721C22×C3—102no—
722C22×C3—102no—
723C22×C3—102no—
724C22×C3—102no—
725C22×C3—102no—
726C22×C3—102no—
727C22×C3—2016no—
728C22×C3—201no—
729C22×C3—201no—
730C22×C3—201no—
731C22×C3—201no—
732C22×C3C22×C4×D511yescharacteristic
733C22×C3#414411yescharacteristic
734C22×C3#414411yescharacteristic
735C22×C3D5×#4111yescharacteristic
736C22×C3D5×#4111yescharacteristic
737C22×C3#414911yescharacteristic
738C22×C3#414911yescharacteristic
739C3×C4—41no—
740C3×C4—41no—
741C3×C4—201no—
742C3×C4—201no—
743Dic3—22no—
744Dic3—22no—
745Dic3—41no—
746Dic3—41no—
747Dic3—102no—
748Dic3—102no—
749Dic3—201no—
750Dic3—201no—
751C2×C5—42no—
752C2×C5C2×#87711yescharacteristic
753C2×C5#548611yescharacteristic
754C2×C5#548611yescharacteristic
755C2×C5#559311yescharacteristic
756C2×C5#559311yescharacteristic
757C2×C5#559311yescharacteristic
758C2×C5#559311yescharacteristic
759D5—24no—
760D5—42no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—52no—
768C23—52no—
769C23—52no—
770C23—52no—
771C23—108no—
772C23—101no—
773C23—101no—
774C23—101no—
775C23—101no—
776C23—101no—
777C23—101no—
778C23—101no—
779C23—101no—
780C23—101no—
781C23—101no—
782C23—204no—
783C23—204no—
784C23—204no—
785C23—204no—
786C23—204no—
787C23—204no—
788C23C4×D3×D512yes—
789C23C22×D3×D511yescharacteristic
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—32no—
797C2×C4—32no—
798C2×C4—61no—
799C2×C4—61no—
800C2×C4—61no—
801C2×C4—61no—
802C2×C4—61no—
803C2×C4—61no—
804C2×C4—61no—
805C2×C4—61no—
806C2×C4—61no—
807C2×C4—61no—
808C2×C4—101no—
809C2×C4—101no—
810C2×C4—101no—
811C2×C4—101no—
812C2×C4—101no—
813C2×C4—101no—
814C2×C4—152no—
815C2×C4—152no—
816C2×C4—301no—
817C2×C4—301no—
818C2×C4—301no—
819C2×C4—301no—
820C2×C4—301no—
821C2×C4—301no—
822C2×C4—301no—
823C2×C4—301no—
824C2×C4—301no—
825C2×C4—301no—
826C2×C4—604no—
827C2×C4—604no—
828C2×C3—42no—
829C2×C3—104no—
830C2×C3—202no—
831C2×C3D5×#11711yescharacteristic
832C2×C3#6587911yescharacteristic
833C2×C3#6587911yescharacteristic
834C2×C3#6594711yescharacteristic
835C2×C3#6599111yescharacteristic
836C2×C3#6601211yescharacteristic
837C2×C3#6603811yescharacteristic
838C5#7382011yescharacteristic, complemented, Sylow
839C22—22no—
840C22—22no—
841C22—22no—
842C22—41no—
843C22—41no—
844C22—41no—
845C22—41no—
846C22—54no—
847C22—102no—
848C22—102no—
849C22—102no—
850C22—102no—
851C22—102no—
852C22—102no—
853C22—102no—
854C22—102no—
855C22—102no—
856C22—2016no—
857C22—201no—
858C22—201no—
859C22—201no—
860C22—201no—
861C22C2×C4×D3×D511yescharacteristic
862C22#9201711yescharacteristic
863C22D5×#23711yescharacteristic
864C22D5×#23711yescharacteristic
865C22#9202511yescharacteristic
866C22#9202611yescharacteristic
867C22#9204911yescharacteristic
868C4—41no—
869C4—41no—
870C4—62no—
871C4—62no—
872C4—121no—
873C4—121no—
874C4—201no—
875C4—201no—
876C4—302no—
877C4—302no—
878C4—601no—
879C4—601no—
880C3#1060755611yescharacteristic, complemented, Sylow
881C2—42no—
882C2—104no—
883C2—202no—
884C2D5×#87711yescharacteristic
885C2#1175292511yescharacteristic
886C2#1175293111yescharacteristic
887C2#1175320011yescharacteristic
888C2#1175462511yescharacteristic
889C2#1175484111yescharacteristic
890C2#1175484611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC24×C3×D5C22
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#2312
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #11751045C2semidirect
3. C5×#4944C2semidirect
6. #11749481C2semidirect
7. #11749478C2semidirect
8. #11748885C2semidirect
9. #11748884C2semidirect
10. #11748878C2semidirect
11. Dic3×#685C2semidirect
12. #11748712C2semidirect
13. #11748709C2semidirect
14. #11748708C2semidirect
15. #11748706C2semidirect
23. C2×#6712C22semidirect
24. C2×C4×Dic15C22semidirect
27. C2×C5×Dic3⋊C4C22semidirect
28. C2×C4×C5×Dic3C22semidirect
34. D5×#217C4semidirect
35. C2×Dic3⋊Dic5C22semidirect
36. C2×#6669C22semidirect
43. C2×Dic3×Dic5C22semidirect
44. C2×Dic3×Dic5C22semidirect
45. #91115C22semidirect
46. #91115C22semidirect
47. C5×C3⋊#95C22semidirect
48. C5×C3⋊#95C22semidirect
49. #90994C22semidirect
50. #90994C22semidirect
51. #90994C22semidirect
52. #90994C22semidirect
131. #4944D5semidirect
263. C2×Dic3⋊C4C2×D5semidirect
267. C2×C4×Dic3C2×D5semidirect
274. C3⋊#95C2×D5semidirect
275. C3⋊#95C2×D5semidirect
709. C3×C5#2312semidirect
838. C5#73820semidirect
880. C3#10607556semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×D5×#2172
#117510452
C5×#49442
C3×#652442
#117494882
#117494812
#117494782
#117488852
#117488842
#117488782
Dic3×#6852
#117487122
#117487092
#117487082
#117487062
#106075563
#738205